Doppler Bins Research Articles

Deep Learning-Based Enhanced ISAR-RID Imaging Method

Inverse synthetic aperture radar (ISAR) imaging can be improved by processing Range-Instantaneous Doppler (RID) images, according to a method proposed in this paper that uses neural networks. ISAR is a significant imaging technique for moving targets. However, scatterers span across several range bins and Doppler bins while imaging a moving target over a large accumulated angle. Defocusing consequently occurs in the results produced by the conventional Range Doppler Algorithm (RDA). Defocusing can be solved with the time-frequency analysis (TFA) method, but the resolution performance is reduced. The proposed method provides the neural network with more details by using a string of RID frames of images as input. As a consequence, it produces better resolution and avoids defocusing. Furthermore, we have developed a positional encoding method that precisely represents pixel positions while taking into account the features of ISAR images. To address the issue of an imbalance in the ratio of pixel count between target and non-target areas in ISAR images, we additionally use the idea of Focal Loss to improve the Mean Squared Error (MSE). We conduct experiments with simulated data of point targets and full-wave simulated data produced by FEKO to assess the efficacy of the proposed approach. The experimental results demonstrate that our approach can improve resolution while preventing defocusing in ISAR images.

Reduction of PAPR in OTFS using rooting companding techniques

ABSTRACT Peak-to-average power ratio (PAPR) is one of the major limitations of an orthogonal time frequency space (OTFS) system. To reduce the PAPR, this paper proposes three companding techniques, namely, logarithmic rooting companding, rooting companding, and rooting-based -law companding. This paper also presents the preferable range of rooting parameter through the analysis of variation of PAPR and bit error rate (BER) with respect to the rooting parameter. To assess the performance of the proposed companding techniques, simulations are carried out by considering various number of delay and Doppler bins. The simulation results reveal that all the proposed techniques provide better PAPR performance than the existing -law companding.

Analysis, Estimation and Compensation of Hardware Impairments for CP-OTFS Systems

Orthogonal time frequency space (OTFS) waveform, which is robust to doubly-selective fading channels is a strong contender for the Fifth generation (5G) communications. At high frequencies, hardware imperfections are prominent in practice at the transceivers. In this letter, we consider impairments such as carrier frequency offset (CFO), direct current (DC) offset and in-phase and quadrature (IQ) imbalance at the transmitter (Tx) and receiver (Rx) for cyclic prefix (CP) OTFS system. We derive the input-output (I/O) relation in the delay-Doppler (DD) domain under these impairments and show that due to the DC offset and IQ imbalance, image Doppler interference (IDI) appears along the Doppler domain and the CFO becomes part of the channel parameters. We estimate impairment parameters in the DD domain and compensate these at Tx and Rx in the time domain. The normalized mean square error (NMSE) of the estimated imbalance parameters are evaluated and it is observed that NMSE reduces with increase in, pilot power, number of Doppler bins and with windowing techniques applied in time-frequency (TF) domain.

Quartic Riemannian Trust Region Algorithm for Cognitive Radar Ambiguity Function Shaping

Waveform adaptation grants cognitive radar (CR) the ability to adapt to its environment, which requires an effective framework to synthesize waveforms sharing a desired ambiguity function (AF). In this letter, we propose a novel method for shaping the slow-time AF in order to adaptively suppress the interference power. The problem is formulated as minimizing the average value of the slow-time AF over some range Doppler bins spanned by the interference, which can be identified exploiting a plurality of knowledge sources. From a technical point of view, this is tantamount to optimizing a complex quartic-order polynomial with a constant modulus (CM) constraint on each optimization variable. To solve this problem, we proposed a quartic Riemannian trust region algorithm. This algorithm first transforms the optimization into an unconstrained one in a complex circle Riemannian manifold, then devises a new Riemannian trust region optimization algorithm that invokes Riemannian gradient and Hessian matrix to obtain an iterative solution with super-linear convergence rate and ability to escape potential saddle points. Simulation results demonstrated that our proposed algorithm outperformed state-of-the art approaches for AF shaping while being computationally less expensive.

A two-step approach to the processing of high-resolution SAR satellite data based on the chirp z-transform

ABSTRACT The processing of high resolution spotlight synthetic aperture radar (SAR) data suffers from Doppler spectrum aliasing because of the limited pulse repetition frequency (PRF). A modified two-step approach (TSA) based on the chirp z-transform (CZT) to high resolution spaceborne SAR data processing is proposed to deal with the spectral aliasing problem in this paper. The range frequency dependent quadratic phase function applied in modified TSA, which can remove the Doppler modulation of the signal completely, gives rise to the effect that the Doppler bin size varies with the range frequency. Thus, the extra spectrum resampling procedure is required to obtain a uniformly sampled signal spectrum. A spectrum resampling approach based on the chirp z-transform is proposed, which can overcome the range frequency dependent distortion. Experiments are performed on simulated point and experimental SAR data to validate the presented approach.

New Channel Errors Estimation Method for Multichannel SAR Based on Virtual Calibration Source

The multichannel synthetic aperture radar (SAR) system can effectively overcome the fundamental limitation between high-resolution and wide-swath. However, the unavoidable channel errors will result in a mismatch of the reconstruction filter and false targets in pairs. To address this issue, a novel channel errors calibration method is proposed based on the idea of minimizing the mean square error (MMSE) between the signal subspace and the space spanned by the practical steering vectors. The practical steering matrix of each Doppler bin can be constructed according to the Doppler spectrum. Compared with the time-domain correlation method, the proposed method no longer depends on the accuracy of the Doppler centroid estimation. Besides, compared with the orthogonal subspace method, the proposed method has the advantage of robustness under the condition of large samples by using the diagonal loading technique. To evaluate the performance, the results of simulation data and the real data acquired by the GF-3 dual-channel SAR system demonstrate that the proposed method has higher accuracy and more robustness than the conventional methods, especially in the case of low SNRs and high non-uniformity.

Sea Clutter Covariance Matrix Estimation and Its Application to Whitening Filter

The accurate estimation of clutter covariance matrix (CCM) is essential in designing a radar detector/filter to suppress sea clutter. This estimation might not be easily accomplished because of the scarcity of valid training vectors adjacent to the range cell under test (CUT). We propose a new CCM estimation algorithm that is derived by modeling time-series clutter returns into a clutter Doppler spectrum in the frequency domain and exploiting mutual independence among spectral components. To justify its excellence over the conventional sample covariance matrix (SCM) algorithm, we design two filters—a maximum signal-to-interference-plus-noise ratio (SINR)-based filter and a whitening filter—that use the estimated CCMs and compare their performance in a numerically simulated sea clutter scenario. Comparisons are made by showing the eigenvector spectra of the estimated CCMs and the frequency responses and outputs of the filters. Moreover, SINRs at the target Doppler bin are examined and compared with a theoretical, analytically derived SINR.

Suppression of Spur Chirps for Fractional-N PLL-Based Heterodyne FMCW SAR

Fractional-N phase-locked loops (PLLs) offer a low-cost solution to the precision frequency ramp requirements of frequency-modulated continuous-wave (FMCW) radar. Regrettably, however, these PLLs are known to produce undesirable spurii in their synthesized output. A subset of these spurii has recently been shown to manifest as frequency chirps, also known as spur chirps , in the deramped beat signal. These so-called spur chirps give rise to Fresnel ripples in the range domain after standard Fourier processing. Spur chirps are of particular concern for heterodyne receiver systems because the Fresnel ripples may appear at levels that far exceed the noise floor. In this article, the authors present guidelines for the avoidance of spur chirps and identify existing interference suppression techniques that are transferable to this problem. Furthermore, the authors put forward a novel technique termed range-Doppler spur masking (RDSM) that was designed specifically for the suppression of spur chirps. The developed technique was applied to both the simulated and measured synthetic aperture radar (SAR) data. Simulations reveal that RDSM significantly outperforms time-domain zeroing in terms of peak sidelobe ratio (PSLR) and other metrics. When applied to the measured data, RDSM is shown to eliminate the effects of the spur chirps in SAR imagery when masking only 0.15% of the available Doppler bins.

A Minimum-Energy-Based Algorithm for Multichannel Reconstruction

For the azimuth multichannel synthetic aperture radar (SAR), nonuniform sampling is common since the pulse-repetition frequency cannot be selected arbitrarily, which leads to the contradiction between ambiguity and noise suppression in the azimuth signal reconstruction. This letter constructs a novel multichannel signal model by taking the coherence among different Doppler bins into account and proposes a minimum-energy-based multichannel reconstruction algorithm, which can obtain the unambiguous signal spectrum without increasing noise in the nonuniform sampling cases. By comparing the simulation results formed by digital beamforming (DBF), improved DBF (IDBF), and space-time adaptive processing (STAP) algorithms, the proposed algorithm shows better performance in balancing ambiguity and noise.

Advanced Sea Surface Target Detection System for Shipborne VHF Radar in Log Periodic Dipole Array Antenna

While navigating in sea target detection is an important problem in modern era communication. In the ocean to detect moving targets and to analyze active variables such as wind, waves and current we can make use of Very High Frequency Ground Wave Radar (VHFGWR). In shipborne VHFGWR the brag spectra widened by Doppler Effect of the ship motion, due to this vessel echo easily merged.An orthogonal projection method to suppress the extended Brag spectra using a log periodic dipole array is proposed in this paper. The advanced technique majorly covers two stages: 1) by utilizing sea echo parameters calculate the approximation of sea clutter in spatial domain and 2) design multi frequency classification Doppler bins method to suppress the extended Brag spectra. After echo suppression, for target detection we can use different algorithms. Simulation result gives a proof that signal- to- clutter noise ratio (SCR) is developed and sea clutter got removed. This method gives very good target detection for shipborne VHF radar.

Low-Complexity Linear Equalization for OTFS Modulation

In this letter, we propose low-complexity linear equalizers for orthogonal time frequency space (OTFS) modulation that exploit the structure of the effective channel matrix in OTFS. The proposed approach exploits the block circulant nature of the OTFS channel matrix to achieve significant complexity reduction. For an $N\times M$ OTFS system, where $N$ and $M$ are the number of Doppler and delay bins, respectively, the proposed approach gives exact minimum mean square error (MMSE) and zero-forcing (ZF) solutions with just $\mathcal {O}(MN \log MN)$ complexity, while MMSE and ZF solutions using the traditional matrix inversion approach require $\mathcal {O}(M^{3}N^{3})$ complexity. The proposed approach can provide low complexity initial solutions for local search techniques to achieve enhanced bit error performance.

The Use of SMAP-Reflectometry in Science Applications: Calibration and Capabilities

The Soil Moisture Active Passive (SMAP) mission became one of the newest spaceborne Global Navigation Satellite System–Reflectometry (GNSS-R) missions collecting Global Positioning System (GPS) bistatic radar measurements when the band-pass center frequency of its radar receiver was switched to the GPS L2C band. SMAP-Reflectometry (SMAP-R) brings a set of unique capabilities, such as polarimetry and improved spatial resolution, that allow for the exploration of scientific applications that other GNSS-R missions cannot address. In order to leverage SMAP-R for scientific applications, a calibration must be performed to account for the characteristics of the SMAP radar receiver and each GPS transmitter. In this study, we analyze the unique characteristics of SMAP-R, as compared to other GNSS-R missions, and present a calibration method for the SMAP-R signals that enables the standardized use of these signals by the scientific community. There are two key calibration parameters that need to be corrected: The first is the GPS transmitted power and GPS antenna gain at the incidence angle of the measured reflections and the second is the convolution of the SMAP high gain antenna pattern and the glistening zone (Earth surface area from where GPS signals scatter). To account for the GPS transmitter variability, GPS instrument properties—transmitted power and antenna gain—are collocated with information collected from the CYclone Global Navigation Satellite System (CYGNSS) at SMAP’s range of incidence angles (37.3° to 42.7°). To account for the convolutional effect of the SMAP antenna gain, both the scattering area of the reflected GPS signal and the SMAP antenna footprint are mapped on the surface. We account for the size of the scattering area corresponding to each delay and Doppler bin of the SMAP-R measurements based off the SMAP antenna pattern, and normalize according to the size of a measurement representative to one obtained with an omnidirectional antenna. We have validated these calibration methods through an analysis of the coherency of the reflected signal over an extensive area of old sea ice having constant surface characteristics over a period of 3 months. By selecting a vicarious scattering surface with high coherency, we eliminated scene variability and complexity in order to avoid scene dependent aliases in the calibration. The calibration method reduced the dependence on the GPS transmitter power and gain from ~1.08 dB/dB to a residual error of about −0.2 dB/dB. Results also showed that the calibration method eliminates the effect of the high gain antenna filtering effect, thus reducing errors as high as 10 dB on angles furthest from SMAP’s constant 40° incidence angle.

Enhanced Detection of Doppler-Spread Targets for FMCW Radar

Frequency-modulated continuous waveform signals are of great interest in automotive radar, perimeter radar, and wide-area surveillance radar applications. For automotive radars and wide-area surveillance radars, which generally utilize high Doppler frequency resolution for target recognition, the important potential target such as a walking person cannot be viewed as a point-like target due to different velocities of the reflection points of a pedestrian. The echoes of such targets have extended Doppler spectrum, and they appear as horizontal lines in the range-Doppler plane, rather than a single point considered in the traditional cases. However, the existing approaches do not make full use of the Doppler-spread characteristic to enhance the detection performance of pedestrians. In this paper, we will show how this characteristic can be used to enhance the detection performance for Doppler-spread targets. The main goal of this paper is pedestrian detection in wide-surveillance radar applications and the proposed approach can also be applied in automotive radar applications. Motivated by the Hough transform, the energies of most Doppler bins corresponding to the target will be accumulated to enhance the detection performance. The questions of how many and which cells should be accumulated in practical applications are discussed in detail. The proposed approach is based on the ordered statistical-constant false alarm rate but tailored to Doppler-spread targets. The detection performance of this algorithm is derived analytically, and verified via practical wide-area surveillance radar signals.

Peak-to-Average Power Ratio of OTFS Modulation

In this letter, we analyze the peak-to-average power ratio (PAPR) of orthogonal time frequency space modulation (OTFS) waveform. Towards this, we consider modulation symbols on an $N\times M$ delay-Doppler grid, where $N$ and $M$ are the number of Doppler and delay bins, respectively. We derive an upper bound on the PAPR of the OTFS signal and show that the maximum PAPR grows linearly with $N$ (and not with $M$ , the number of subcarriers, as observed in conventional multicarrier schemes such as OFDM). We analytically characterize the complementary cumulative distribution function (CCDF) of the PAPR of OTFS with rectangular pulse for large values of $N$ . We present the simulated CCDF of the PAPR of OTFS for different pulse shapes and compare it with those of OFDM and generalized frequency division multiplexing (GFDM). It is shown that OTFS can have better PAPR compared to OFDM and GFDM.

Sea Clutter Suppression for Shipborne HF Radar Using Cross-Loop/Monopole Array

The shipborne high-frequency ground wave radar (HFGWR) provides a better condition for sea surface target detection than the shore-based one because of its maneuverability and flexibility. However, the first-order Bragg spectra of the shipborne HFGWR would be broadened by the Doppler shift of the ship motion, which makes the vessel echo easily submerged. Even though some methods have been applied to suppress the broadened Bragg spectra for target detection, most of them are hard to achieve good result in a small-aperture radar. An orthogonal projection method to suppress the broadened Bragg spectra using a cross-loop/monopole array is proposed in this letter. The proposed method mainly includes two steps: 1) estimate the space of sea clutter in a spatial domain according to the ocean echo characteristics and 2) design an adaptive filter of single or multiple Doppler bins on the estimated clutter space to suppress the first-order spectra. After suppression, we use the multiple signal classification algorithm to estimate the incident direction of targets. The experimental data validate that the sea clutter is well suppressed and the target signal-to-clutter ratio is increased by the algorithm.

Detecting Sea Ice From TechDemoSat-1 Data Using Support Vector Machines With Feature Selection

In this paper, a framework that employs support vector machines (SVMs) is proposed for the classification of TechDemoSat-1 delay-Doppler maps (DDMs), specifically, for separating DDMs of sea ice from those of seawater. DDM data were first operated with a general data preprocessing procedure, which included noise floor subtraction and normalization. In addition, a simple and effective feature selection (FS) was devised so that the input size was significantly reduced (from 128 × 20 to 20) while the classification accuracy was enhanced. To be specific, the feature was selected as the mean value along the delay-axis (128 in length) at each Doppler bin (20 in all). Here, expected classification labels (sea ice/seawater) were obtained based on reference sea ice concentration data collected by multiple passive microwave sensors. In practice, this trained SVMs-FS algorithm showed improved accuracy but less data storage demands than the existing neural networks (NNs)- and convolutional neural networks-based methods. In addition, the designed FS was also proven to be effective for both SVMs and NNs.

Adaptive reconstruction for azimuth signal of multichannel HRWS SAR imaging system

The reconstruction of azimuth signal in multichannel synthetic aperture radar (SAR) for high-resolution and wide-swath (HRWS) imaging requires exact steering vectors. The information of ambiguities and system parameters are used to create the steering vectors. The knowledge of ambiguities involves ambiguity number and index; the system parameters include the pulse repetition frequency (PRF), platform velocity, and channel spacing. However, in some cases, the knowledge of ambiguities is Doppler-variant and there exist errors in the system parameters, which may degrade the reconstruction performance. In this work, an adaptive reconstruction method is developed. Firstly, we discuss the azimuth sampling of multichannel SAR and derive the equation of ambiguity index. We then utilize the azimuth cross-correlation to determine the aliasing number. Afterwards, based on the spatial spectrum estimation methods, an equivalent system parameter is adaptively calculated. With the aliasing number and the equivalent parameter, we can obtain the ambiguity information of each Doppler bin. Therefore, the steering vectors are constructed and the azimuth ambiguities can be suppressed. Compared with state-of-the-art reconstruction methods, our method achieves excellent performance even in highly nonuniform sampling case. Without relying on any system parameters, the proposed method has better practicality and applicability. We conduct extensive experiments including simulations and real data processing to verify the effectiveness and evaluate the performance of the proposed method.

Training-Based Adaptive Transmit–Receive Beamforming for MIMO Radars

The recent advancements in digital control of the waveforms transmitted by radar systems has enabled implementation of multiple-input multiple-output radar systems. In such radars, each element is capable of transmitting a different waveform; in this paper, we focus on modifying a multiplicative weight at each transmitter to improve detection performance. Several authors have considered the problem of optimizing the transmit weights and the receive filter generally to maximize the output signal-to-interference-plus-noise ratio. Crucially, these previous works assumed a priori knowledge of the required second-order statistics. In this regard, we make two key contributions: First, we formulate and solve an optimization problem to estimate these required statistics using only signals received in previous coherent processing intervals (CPIs). Essentially, we estimate the transmit interference covariance matrix using receive data. The estimation does not assume any specific structure for the clutter covariance matrix. By using the most recent CPIs in the design, our approach makes it possible to track changes in the interference environment, and, therefore, adaptively design the transmit code in real time. Second, we introduce reduced-dimension processing for transmit adaptivity. As in the case of receive space-time adaptive processing (STAP), it is crucial to be able to perform filter design with only a limited number of available training samples. While reduced-dimension processing is well established for receive adaptivity, as we will see, transmit reduced-dimension processing requires a completely different formulation. We consider transmit code design for a single look angle-Doppler bin and also for a range of Doppler bins in the case that the target Doppler shift is unknown. Finally, we present simulation results, in the context of phase-perturbed propagation and airborne radars, to illustrate the performance of the proposed methods.

Local Ambiguity Function Shaping via Unimodular Sequence Design

This letter focuses on the local ambiguity function shaping through unimodular sequence design. An accelerated iterative sequential optimization (AISO) algorithm is proposed to minimize the average value of the weighted integrated sidelobe level (WISL) over specific Doppler bins and range bins of interest. We evaluate the effectiveness of the AISO algorithm in terms of its achieved WISL and computational complexity in comparison with the gradient method via numerical examples. The capability of using the design to detect high-speed targets is also evaluated.

An adaptive sequential estimation algorithm for velocity jamming suppression

In this paper, we consider the moving target detection problem for a Pulse Doppler (PD) radar in the presence of multiple velocity jamming. Exploiting the observation that the repeater jamming often contaminates more than one radar pulse, we present an adaptive sequential estimation algorithm to obtain simultaneously the target and jamming profiles in the Doppler domain. At each iteration, employing the estimated Doppler profiles of targets and jamming obtained at the previous iteration, the optimal linear filters are designed to minimize the output average power for each Doppler bin. The presented sequential estimation algorithm yields very low Doppler side lobes and the jamming velocities are eliminated in the Doppler profiles of targets. Finally, we evaluate the performance of the proposed technique as well as the Matched Filter (MF) method via numerical simulations.